- Treffer 1 von 1
Partial clones
- A set C of operations defined on a nonempty set A is said to be a clone if C is closed under composition of operations and contains all projection mappings. The concept of a clone belongs to the algebraic main concepts and has important applications in Computer Science. A clone can also be regarded as a many-sorted algebra where the sorts are the n-ary operations defined on set A for all natural numbers n >= 1 and the operations are the so-called superposition operations S-m(n) for natural numbers m, n >= 1 and the projection operations as nullary operations. Clones generalize monoids of transformations defined on set A and satisfy three clone axioms. The most important axiom is the superassociative law, a generalization of the associative law. If the superposition operations are partial, i.e. not everywhere defined, instead of the many-sorted clone algebra, one obtains partial many-sorted algebras, the partial clones. Linear terms, linear tree languages or linear formulas form partial clones. In this paper, we give a survey onA set C of operations defined on a nonempty set A is said to be a clone if C is closed under composition of operations and contains all projection mappings. The concept of a clone belongs to the algebraic main concepts and has important applications in Computer Science. A clone can also be regarded as a many-sorted algebra where the sorts are the n-ary operations defined on set A for all natural numbers n >= 1 and the operations are the so-called superposition operations S-m(n) for natural numbers m, n >= 1 and the projection operations as nullary operations. Clones generalize monoids of transformations defined on set A and satisfy three clone axioms. The most important axiom is the superassociative law, a generalization of the associative law. If the superposition operations are partial, i.e. not everywhere defined, instead of the many-sorted clone algebra, one obtains partial many-sorted algebras, the partial clones. Linear terms, linear tree languages or linear formulas form partial clones. In this paper, we give a survey on partial clones and their properties.…
Verfasserangaben: | Klaus-Dieter DeneckeORCiDGND |
---|---|
DOI: | https://doi.org/10.1142/S1793557120501612 |
ISSN: | 1793-5571 |
ISSN: | 1793-7183 |
Titel des übergeordneten Werks (Englisch): | Asian-European journal of mathematics : AEJM |
Verlag: | World Scientific |
Verlagsort: | Singapore |
Publikationstyp: | Wissenschaftlicher Artikel |
Sprache: | Englisch |
Datum der Erstveröffentlichung: | 28.05.2020 |
Erscheinungsjahr: | 2020 |
Datum der Freischaltung: | 12.01.2023 |
Freies Schlagwort / Tag: | Operation; clone; dht-symmetric category; formula; formulas; linear formula; linear hypersubstitution; linear term; linear tree language; partial; partial clone; superposition of operations; term; terms and; theory |
Band: | 13 |
Ausgabe: | 8 |
Aufsatznummer: | 2050161 |
Seitenanzahl: | 19 |
Organisationseinheiten: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
DDC-Klassifikation: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
Peer Review: | Referiert |